Symbolic Propagation and Sensitivity Analysis in Gaussian Bayesian Networks with Application to Damage Assessment E. Castillo 1 , J. M. Guti´ errez 1 , A. S. Hadi 2 and C. Solares 1 1 Department of Applied Mathematics and Computational Sciences, University of Cantabria, SPAIN 2 Department of Statistics, Cornell University, USA ABSTRACT In this paper we show how Bayesian network models can be used to perform a sen- sitivity analysis using symbolic, as opposed to numeric, computations. An example of damage assessment of concrete structures of buildings is used for illustrative pur- poses. Initially,normalorGaussianBayesiannetworkmodelsaredescribedtogether with an algorithm for numerical propagation of uncertainty in an incremental form. Next,thealgorithmisimplementedsymbolically,inMathematicacode,andapplied to answer some queries related to the damage assessment of concrete structures of buildings. Finally, the conditional means and variances of the of nodes given the evidence are shown to be rational functions of the parameters, thus, discovering its parametric structure, which can be efficiently used in sensitivity analysis. Key Words: Expert systems, Multivariate normal distribution, Symbolic computa- tions. 1 Introduction In recent years much attention has been focussed on the use of probabilistic mod- els in expert systems. Today, probabilistic models, especially those associated with Bayesian networks, are gaining more and more popularity as a formalism for han- dling uncertainty. The increasing number of applications in the last few years also show that this formalism has practical value (an ever growing list of applications in several disciplines: Medicine, Engineering, etc., is available by anonymous FTP from: research.microsoft.com:/pub/dtg/bn-apps.ps). OneofthekeyproblemsinBayesiannetworksisevidencepropagation,whichcon- sists of updating the the posterior probabilities of a set of variables of interest when- ever a new evidence becomes available. There exist several well known algorithms for the exact and approximate propagation of evidence in Bayesian networks 1-6 . How- ever,fromapracticalpointofview,mostofthesemethodsarerestrictivebecausethey require all variables to be discrete, while many examples arising in practice involve continuous variables. 1